# Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration

arXiv: https://arxiv.org/abs/2102.12182 · HTML: https://mlsanity.com/paper/2102.12182/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 269 references that are in the map.
- First posted on arXiv 24 Feb 2021.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Calibration of Neural Networks using Splines](https://mlsanity.com/paper/2006.12800/) (2020)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Non-Parametric Calibration for Classification](https://mlsanity.com/paper/1906.04933/) (2019)
- [The Double Sphere Camera Model](https://mlsanity.com/paper/1807.08957/) (2018)
- [Dirichlet-based Gaussian Processes for Large-scale Calibrated Classification](https://mlsanity.com/paper/1805.10915/) (2018)
- [What Makes Good Synthetic Training Data for Learning Disparity and Optical Flow Estimation?](https://mlsanity.com/paper/1801.06397/) (2018)
- [Associative Domain Adaptation](https://mlsanity.com/paper/1708.00938/) (2017)
- [Learning by Association - A versatile semi-supervised training method for neural networks](https://mlsanity.com/paper/1706.00909/) (2017)
- [Efficient Online Surface Correction for Real-time Large-Scale 3D Reconstruction](https://mlsanity.com/paper/1709.03763/) (2017)
- [Point-wise Map Recovery and Refinement from Functional Correspondence](https://mlsanity.com/paper/1506.05603/) (2015)
- [Spectral Decompositions using One-Homogeneous Functionals](https://mlsanity.com/paper/1601.02912/) (2016)
- [A Variational Approach to Shape-from-shading Under Natural Illumination](https://mlsanity.com/paper/1709.10354/) (2017)
- [Collaborative Total Variation: A General Framework for Vectorial TV Models](https://mlsanity.com/paper/1508.01308/) (2015)
- [A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching](https://mlsanity.com/paper/1611.05241/) (2016)
- [Dense Multi-view 3D-reconstruction Without Dense Correspondences](https://mlsanity.com/paper/1704.00337/) (2017)

## Built on by (most cited first, 30 of 48)

- [ConfTuner: Training Large Language Models to Express Their Confidence Verbally](https://mlsanity.com/paper/2508.18847/) (2025)
- [Robust Calibration of Large Vision-Language Adapters](https://mlsanity.com/paper/2407.13588/) (2024)
- [Adaptive Temperature Scaling for Robust Calibration of Deep Neural Networks](https://mlsanity.com/paper/2208.00461/) (2022)
- [Proximity-Informed Calibration for Deep Neural Networks](https://mlsanity.com/paper/2306.04590/) (2023)
- [How to Fix a Broken Confidence Estimator: Evaluating Post-hoc Methods for Selective Classification with Deep Neural Networks](https://mlsanity.com/paper/2305.15508/) (2023)
- [ACLS: Adaptive and Conditional Label Smoothing for Network Calibration](https://mlsanity.com/paper/2308.11911/) (2023)
- [Open-Vocabulary Calibration for Fine-tuned CLIP](https://mlsanity.com/paper/2402.04655/) (2024)
- [Beyond In-Domain Scenarios: Robust Density-Aware Calibration](https://mlsanity.com/paper/2302.05118/) (2023)
- [Understanding and Mitigating Miscalibration in Prompt Tuning for Vision-Language Models](https://mlsanity.com/paper/2410.02681/) (2024)
- [Feature Clipping for Uncertainty Calibration](https://mlsanity.com/paper/2410.19796/) (2024)
- [Scaling of Class-wise Training Losses for Post-hoc Calibration](https://mlsanity.com/paper/2306.10989/) (2023)
- [Optimizing Calibration by Gaining Aware of Prediction Correctness](https://mlsanity.com/paper/2404.13016/) (2024)
- [Uncertainty Calibration with Energy Based Instance-wise Scaling in the Wild Dataset](https://mlsanity.com/paper/2407.12330/) (2024)
- [Accuracy-Preserving Calibration via Statistical Modeling on Probability Simplex](https://mlsanity.com/paper/2402.13765/) (2024)
- [Decoupling of neural network calibration measures](https://mlsanity.com/paper/2406.02411/) (2024)
- [Consistency Calibration: Improving Uncertainty Calibration via Consistency among Perturbed Neighbors](https://mlsanity.com/paper/2410.12295/) (2024)
- [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024)
- [Enhancing Out-of-Distribution Detection with Extended Logit Normalization](https://mlsanity.com/paper/2504.11434/) (2025)
- [Sample Margin-Aware Recalibration of Temperature Scaling](https://mlsanity.com/paper/2506.23492/) (2025)
- [Sensitivity analysis of AI-based algorithms for autonomous driving on optical wavefront aberrations induced by the windshield](https://mlsanity.com/paper/2308.11711/) (2023)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Quantile Adaptive Temperature Scaling for Confidence Calibration](https://mlsanity.com/paper/2606.21749/) (2026)
- [Perception and Semantic Aware Regularization for Sequential Confidence Calibration](https://mlsanity.com/paper/2305.19498/) (2023)
- [IW-GAE: Importance Weighted Group Accuracy Estimation for Improved Calibration and Model Selection in Unsupervised Domain Adaptation](https://mlsanity.com/paper/2310.10611/) (2023)
- [Tilt and Average : Geometric Adjustment of the Last Layer for Recalibration](https://mlsanity.com/paper/2406.10017/) (2024)
- [Classifier Ensemble for Efficient Uncertainty Calibration of Deep Neural Networks for Image Classification](https://mlsanity.com/paper/2501.10089/) (2025)
- [Adaptive Cumulative Mass Calibration with Conformal Prediction](https://mlsanity.com/paper/2505.15437/) (2025)
- [Beyond Overconfidence: Foundation Models Redefine Calibration in Deep Neural Networks](https://mlsanity.com/paper/2506.09593/) (2025)
- [Probability Bounding: Post-Hoc Calibration via Box-Constrained Softmax](https://mlsanity.com/paper/2506.10572/) (2025)
- [Instance-Wise Monotonic Calibration by Constrained Transformation](https://mlsanity.com/paper/2507.06516/) (2025)

## Abstract (arXiv)

We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated confidence scores using post-hoc calibration methods. In this contribution, we demonstrate that the performance of accuracy-preserving state-of-the-art post-hoc calibrators is limited by their intrinsic expressive power. We generalize temperature scaling by computing prediction-specific temperatures, parameterized by a neural network. We show with extensive experiments that our novel accuracy-preserving approach consistently outperforms existing algorithms across a large number of model architectures, datasets and metrics.